Crashes and Collateralized Lending

by Jakub W. Jurek & Erik Stafford

Executive Summary — This paper presents a framework for understanding the contribution of systematic crash risk to the cost of capital for a variety of different types of securities. The framework isolates the systematic crash risk exposure of different collateral types (equities, corporate bonds, and CDO tranches), and provides a simple mechanism for allocating the cost of bearing this risk between a financing intermediary and investor. Research was conducted by Jakub W. Jurek (Bendheim Center for Finance, Princeton University) and Erik Stafford (Harvard Business School). Key concepts include:

A typical loan extended by a broker to an investor for a purchase on margin is collateralized by the underlying security and protected by the investor's capital contribution (the collateral, margin, or "haircut"). The haircut protects the intermediary from changes in the liquidation value of the collateral.

The researchers' focus is looking at haircuts as an effective protection against large market declines.

They derive a schedule of haircuts and financing rates (spreads above the risk-free rate), which represents the intermediary's fair charge for providing leverage to the investor.

The framework also can be used to stress test different types of collateral by examining the predicted financing terms as market conditions change.

This systematic credit risk channel has not been explored in the banking literature, despite the growing role of collateralized borrowing in the economy (e.g. repo market) and the seeming relevance of ensuring collateral robustness in adverse economic states.

Author Abstract

This paper develops a parsimonious static model for characterizing financing terms in collateralized borrowing markets. We characterize the systematic risk exposures for a variety of securities and develop a simple indifference-pricing framework to value the systematic crash risk exposure of the collateral. We then apply Modigliani and Miller's (1958) Proposition Two (MM) to split the cost of bearing this risk between the investor and the intermediary broker, resulting in a schedule of haircuts and financing rates. The model produces comparative statics and time-series dynamics that are consistent with the empirical features of repo market data, including the credit crisis of 2007-2008.